341review-part2 - Math 341 Review Fall 2010 2 Linear...

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Math 341 Review — Fall 2010 2. Linear algebra This topic covered parts of Chapters 1, 2, 3, and 6 of the Leon book. A good way to review is to do particular problems. 1. Solve the following systems or show that they are inconsistent. 1a. x 1 - 2 x 2 = 5 3 x 1 + x 2 = 1 1b. 4 x 1 + 3 x 2 = 4 2 3 x 1 + 4 x 2 = 3 1
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1c. 2 x 1 - 3 x 2 = 5 - 4 x 1 + 6 x 2 = 8 1d. x 1 + x 2 = 0 2 x 1 + 3 x 2 = 0 3 x 1 - 2 x 2 = 0 1e. 2 x 1 + 3 x 2 + x 3 = 1 x 1 + x 2 + x 3 = 3 3 x 1 + 4 x 2 + 2 x 3 = 4 2
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2. Compute the following determinants (using whatever method you think is most appropriate). 2a. 3 1 2 2 5 4 2 5 4 2b. 1 3 2 4 1 - 2 2 1 3 2c. 2 0 0 1 0 1 0 0 1 6 2 0 1 1 - 2 3 3
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3. Find all possible values of c that would make the matrix nonsingular: 1 1 1 1 9 c 1 c 3 4. Which of the following are spanning sets for R 3 ? 4a. (1 , 0 , 0) T , (0 , 1 , 1) T , (1 , 0 , 1) T , (1 , 2 , 3) T 4b. (2 , 1 , - 2) T , (3 , 2 , - 2) T , (2 , 2 , 0) T 4
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5. Which of the following sets are linearly independent in R 3 ? 5a. (1 , 0 , 0) T , (0 , 1 , 1) T , (1 , 0 , 1) T 5b. (1 , 0 , 0) T , (0 , 1 , 1) T , (1 , 0 , 1) T , (1 , 2 , 3) T 5c. (2 , 1 , - 2) T , (3 , 2 , - 2) T , (2 , 2 , 0) T 5
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6. The five vectors v 1 = 1 2 2 , v 2 = 2 5 4 , v 3
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